Mathematical Morphology and Tropical Geometry share the same max/min-plus scalar arithmetic and matrix algebra. In this paper we summarize their common ideas and algebraic structure, generalize and extend both of them using weighted lattices and a maxalgebra with an arbitrary binary operation that distributes over max, and outline applications to geometry, image analysis, and optimization. Further, we outline the optimal solution of maxequations using weighted lattice adjunctions, and apply it to optimal regression for fitting maxtropical curves on arbitrary data.